This paper considers the problem of mimetic staggered-grid finite difference scheme construction in the case of a boundary misaligned with the grid points. We show that depending on the reciprocal positions of the nearest grid point and whether the point is inside or outside the domain, two cases should be considered separately. In both cases, we present general rules to construct the mimetic difference operators to approximate the gradient and divergence operators. In addition, we investigate the stability criterion of the explicit in time scheme, which employs derived operators to approximate spatial derivatives. We show that, depending on the reciprocal positions of the nearest grid point, the Courant number may be smaller by 7% than that of the initial value problem approximation.